Well, considering that Jo got her kicks dreaming of taking down mythic beasts that would cause most people to soil themselves upon either realization of their existence or upon actual sight, Morpheus wasn't all that surprised to hear her say something like that. But that didn't mean he had to like hearing it.
As for his name, Morpheus considered.
In the Waking World, before Nanshe and before (and in between) Makaria, Morpheus was adept at getting mortal women to sleep with him. Now, he didn't walk around saying he was the god of dreams. Those things got you put away in a nice bouncy cell, and they never let you out--even if you were a god of some kind. No.
In those instances, he'd gone by a variety of aliases, and he even had fake i.d.s for one of them, so that he could enjoy New Orleans all the better. But he did not think that lying to this girl was a good idea. There was something about her, for one, some kind of something just beneath the surface...
But if he was right, if this situation was right and they were all stuck here, which the impression he got from Jo's dream, though they'd not discussed it directly, as well as the impression he was getting from Annabelle's words and the beings in the room with them...
... it was better not to lie to someone in the same situation as he was. As they were.